On the bifurcations occuring in the parameter space of the sixteen vertex model

The 16-dimensional parameter space of homogeneous sixteen vertex models is scanned for bifurcation points, i.e. points corresponding to models which possess extra symmetries not existing in nearby points. Equivalence classes of models having the same partition function are identified by means of a characteristic “normal” model, represented by a (4 x 4)-diagonal matrix N, and a pair of (2 x 2)-matrices A and B. In this paper the matrix N is assumed to be non-degenerate and the only bifurcations found are those associated with special types of matrices A and B, i.e. matrices whose decomposition in terms of Pauli-matrices corresponds to a vector a ≡ (a1, a2, a3) or b ≡ (b1, b2, b3) that is invariant with respect to one or more elements of the cubic symmetry group.